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The concept of monoidal category does not presume that values of such aggregate types can be taken apart; on the contrary, it provides a framework that unifies classical and quantum information theory. [1] In category theory, monoidal categories can be used to define the concept of a monoid object and an associated action on the objects of the ...
In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is an object M together with two morphisms. μ: M ⊗ M → M called multiplication, η: I → M called unit, such that the pentagon diagram. and the unitor diagram commute.
Print/export Download as PDF; Printable version; ... In category theory, a traced monoidal category is a category with some extra structure which gives a ...
A symmetric monoidal category is a monoidal category (C, ⊗, I) such that, for every pair A, B of objects in C, there is an isomorphism : called the swap map [1] that is natural in both A and B and such that the following diagrams commute: The unit coherence: The associativity coherence:
Download as PDF; Printable version; In other projects Wikimedia Commons; Wikidata item; ... Center (category theory) Closed monoidal category; Compact closed category; D.
We have described closed monoidal categories as monoidal categories with an extra property. One can equivalently define a closed monoidal category to be a closed category with an extra property. Namely, we can demand the existence of a tensor product that is left adjoint to the internal Hom functor .
Download as PDF; Printable version; ... In category theory, a (strict) n-monoid is an n ... monoid and a 2-monoid is a strict monoidal category ...
Download as PDF; Printable version; ... Category theory is a mathematical theory that deals in an abstract way with mathematical ... Cartesian monoidal category;